I try to solve the differential equation
DSolve[{3*y[x] + 2*x*y[x]^2 + (2*x + 3*x^2*y[x])*y'[x] == 0, y[1] == 1/2}, y[x], x]
This produces some error messages as
DSolve::bvnul: For some branches of the general solution, the given boundary conditions lead to an empty solution.
It also produces:
$$y(x)\to \text{Root}\left[-8 \text{$\#$1}^5+\frac{40 \text{$\#$1}^4}{x}-\frac{80 \text{$\#$1}^3}{x^2}+\text{$\#$1}^2 \left(\frac{80}{x^3}-\frac{1}{x^2}\right)-\frac{40 \text{$\#$1}}{x^4}+\frac{8}{x^5}\&,1\right]$$
I know this DEQ is solvable because I did it by hand (see implicit solution: https://math.stackexchange.com/questions/2140226/exact-de-y2xy3dxx3xy2dy-0/2140279#2140279) and verified it using WA.
Is there any way to coax Mathematica to produce that result using DSolve
in spite of that nasty IC?
I am using Windows 7, MMA version $11.0.1.0$.
y(x)
in three of thelog
terms. Are you sure there is a solution for this ODE? $\endgroup$